 Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.  The Cambridge Examiner - Сторінка 1211884Повний перегляд - Докладніше про цю книгу
 | Euclides - 1840 - 192 стор.
...the given figure, and similarly situated (vi.Def.i). PROP. XIX. THEOR. Similar triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous sides. Let A, D be equal angles, and AB, DE homologous sides of the similar triangles ABC, DEF ; and on AB,... | |
 | Joseph Denison - 1841 - 210 стор.
...other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous... | |
 | Joseph Denison - 1841 - 210 стор.
...other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their homologous... | |
 | Euclides - 1841 - 378 стор.
...GN. Join BE, AM, GL, FN. And because the polygon ABCDE is similar to the polygon FGHKL, and because similar polygons may be divided into the same number of similar triangles; the triangles ABE, FGL, are similar and equiangular;* and therefore the angle * 20. 6. AEB is equal... | |
 | John Playfair - 1842 - 332 стор.
...triangle upon the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. Similar polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL,... | |
 | Euclides - 1842 - 316 стор.
...triangle upon the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Draw BE, EC, GL,... | |
 | William Pease - 1843 - 80 стор.
...similar polygon, equal to the sum of the given polygons. For, " universally, similar'rectilineal figures are to one another in the duplicate ratio of their homologous sides." Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make... | |
 | 1844 - 688 стор.
...of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3.... | |
 | 1844 - 456 стор.
...chord will be bisected at right angles by a straight line joining their centres. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. About the centre of a given circle describe another circle, equal in area to half the former. TRIGONOMETRY... | |
 | Euclides - 1845 - 546 стор.
...upon the first to a similar and similarly described triangle upon the second. PROPOSITION XX. THEOREM. Similar polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
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